Final answer:
Option D, y = (x+1)² - 1, is the correct answer as it represents a parabola with a vertex at (-1, -1), matching the vertex form y = a(x - h)² + k.
Step-by-step explanation:
The question asks which equation represents a parabola with a vertex at (-1, -1). To identify this equation, we should look for a vertex form of a parabola's equation, which is generally expressed as y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Looking at the options given:
• A) y = (x - 1)² +1
• B) y = (x - 1)² -1
• C) y = (x+1)² +1
• D) y = (x+1)² - 1
The vertex form indicates that the h value is taken from the expression (x - h), which suggests that the h value is positive in case it appears as (x +1) after rearranging. Therefore, options A and B are immediately ruled out as they would have a vertex at (1, k). Between options C and D, since the vertex has a y-coordinate of -1, we look for k to be -1, which is present in option D. Hence, option D is the correct answer as it is the equation that represents a parabola with a vertex at (-1, -1).